An enquiry into the budget of the middle class families in a city in England gave the following information:
What is the cost of living index of 2004 as compared with that of 1995 are seen?

Answer

To find the cost of living index of 2004 as compared with that of 1995, we will follow these steps:

### Step 1: Gather the data
We have the expenses for different categories in both years (2004 and 1995).

- **2004 Expenses (p1)**:
- Food: 1500
- Fuel: 250
- Clothing: 750
- Rent: 300
- Miscellaneous: 400

- **1995 Expenses (p0)**:
- Food: 1400
- Fuel: 200
- Clothing: 500
- Rent: 200
- Miscellaneous: 250

### Step 2: Assign weights (w)
The weights represent the proportion of total expenses for each category. For our calculation, we will assume the weights are as follows:
- Food: 35%
- Fuel: 10%
- Clothing: 20%
- Rent: 15%
- Miscellaneous: 20%

### Step 3: Create a table
We will create a table to organize our data:

| Category | p0 (1995) | p1 (2004) | R = (p1/p0) * 100 | w (%) | Rw = R * w |
|------------------|-----------|-----------|--------------------|-------|------------|
| Food | 1400 | 1500 | (1500/1400) * 100 | 35 | |
| Fuel | 200 | 250 | (250/200) * 100 | 10 | |
| Clothing | 500 | 750 | (750/500) * 100 | 20 | |
| Rent | 200 | 300 | (300/200) * 100 | 15 | |
| Miscellaneous | 250 | 400 | (400/250) * 100 | 20 | |

### Step 4: Calculate R for each category
Now we will calculate R for each category:

1. **Food**:
\[ R = \left(\frac{1500}{1400}\right) \times 100 = 107.14 \]

2. **Fuel**:
\[ R = \left(\frac{250}{200}\right) \times 100 = 125 \]

3. **Clothing**:
\[ R = \left(\frac{750}{500}\right) \times 100 = 150 \]

4. **Rent**:
\[ R = \left(\frac{300}{200}\right) \times 100 = 150 \]

5. **Miscellaneous**:
\[ R = \left(\frac{400}{250}\right) \times 100 = 160 \]

### Step 5: Calculate Rw for each category
Now we will calculate Rw for each category by multiplying R by w:

1. **Food**:
\[ Rw = 107.14 \times 35 = 3750 \]

2. **Fuel**:
\[ Rw = 125 \times 10 = 1250 \]

3. **Clothing**:
\[ Rw = 150 \times 20 = 3000 \]

4. **Rent**:
\[ Rw = 150 \times 15 = 2250 \]

5. **Miscellaneous**:
\[ Rw = 160 \times 20 = 3200 \]

### Step 6: Sum up the weights and Rw
Now we will sum up the weights and Rw:

- **Total weight (Σw)**:
\[ 35 + 10 + 20 + 15 + 20 = 100 \]

- **Total Rw (ΣRw)**:
\[ 3750 + 1250 + 3000 + 2250 + 3200 = 13450 \]

### Step 7: Calculate the Cost of Living Index
Finally, we can calculate the cost of living index using the formula:

\[ \text{Cost of Living Index} = \frac{\Sigma Rw}{\Sigma w} = \frac{13450}{100} = 134.50 \]

### Final Answer
The cost of living index of 2004 as compared with that of 1995 is **134.50**.

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